Of the “Real Ivies”, Columbia, Cornell, and Penn have limitations on internal transfers to some majors or divisions, and presumably differing levels of frosh admission selectivity based on majors or divisions.
Harvard, Yale, and Princeton are among the very wealthy schools which can maintain sufficient extra capacity in all majors and on the campus as a whole to allow declaration or changing major without any barriers other than perhaps remaining in good academic standing and having taken the prerequisites that will result in on-time graduation in the major.